Question

If in two circles arc of the same length subtaned angles 60degree and 75degree at the centre find the racio of their radius

Answer 1

Let the length of the circle be llAngle of the circle 1 =60∘60∘Angle of the circle 2 =75∘75∘Let the radius be r1r1 and r2r2l=r1θl=r1θ⇒r1×60×π180⇒r1×60×π180⇒πr13⇒πr13l=r2θl=r2θ⇒r2×75×π180⇒r2×75×π180⇒5πr212⇒5πr212Since ll is same for both the circles⇒πr13=5πr212⇒πr13=5πr212⇒r1:r2=5:4⇒r1:r2=5:4Hence (A) is the correct answer.
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